Schidlof was born in Vienna, but had to leave Austria when the Nazis came. He went to Great Britain. Because he was musically talented he won a scholarship to Blundell's School in Devon, but when World War II broke out he was interned. It was in the internment camp that met Norbert Brainin and Siegmund Nissel. They often played music together. When they were freed they became pupils of Max Rostal who persuaded Schidlof to play the viola instead of the violin. Together with Martin Lovett the four men formed a string quartet which at first they called the Brainin Quartet, but they soon changed the name to Amadeus Quartet. The Amadeus Quartet gave their first concert at the Wigmore Hall in 1948. Soon they became world famous, playing in concerts and festivals in many countries.
Schidlof was a calm man who listened very carefully to everything that was going on. The others called him "Eagle ears". The four men played together for nearly 40 years until Schidlof's death.